sin(3x)+sin(x)=0 solve for x
Answer:
[tex]x=k\frac\pi2; k\in \mathbb{Z}[/tex]
Step-by-step explanation:
Let's use the formulas that change a sum of two sines into a product:
[tex]sin\ p + sin\ q =2 sin{\frac{p+q}2}cos{\frac{p-q}2}[/tex]
[tex]sin 3x+sinx =2sin \frac{3x+x}2 cos \frac{3x-x}2 = 2(sin2x)(cosx)=0[/tex]
At this point it's either [tex]sin 2x =0 \implies 2x= k\pi \rightarrow x = k\frac{\pi}2[/tex]
or [tex]cosx=0 \rightarrow x=\frac\pi2+ k\pi = (2k+1)\frac\pi2[/tex]
with the usual condition of [tex]k\in \mathbb{Z}[/tex].
Now if you look at both sets of solutions, first one considers all multiples of [tex]\frac\pi2[/tex], while the second only the odd multiples. it means that the first includes the second.
I want to know my grade if I have an 86 and I get a 0 and it’s worth 20% of my grade what will my grade be?
Answer:
your grade will be an 76
Step-by-step explanation:
Can somebody please help me with this true or false algebra 1 question?
A relation that pairs each input with exactly one output is a function.
True or False
I'll help.
The answer to your question is True!!
The game starts as follows. You pick one medal without unwrapping it, and then the game host unwraps one of the remaining medals and reveals that it is a silver medal. (Assume here that the host unwraps a medal with equal probability, but knowing where the gold medal was and avoiding unwrapping the gold medal if still on the table, to keep the game interesting to watch until the end.) You have now three medals left to unwrap (one in your hand, two on the table). At this point, the host gives you the option to change your mind and swap your medal for one of the two left on the table. What would you do at this point? Would you keep your medal, or swap it with one of the two medals left on the table? If so, which one?
Answer:
I'd swap with one on the table (the left one) but with my luck it would be a sword made of rubber
Which of the following is the figure most likely the graph of?
A) f(x) = (2/3)x
B)f(x) = –2x
C)f(x) = (3/2)x
D)f(x) = 2x
The accurate line represented by line b because during such experiment ( osmosis or mass transfer) there would be a time where the system be in equilibrium meaning that that the net movement will be zero. In line B at time starting 15 min equilibrium is reached no further movement is attained beyond it.
I NEED HELP WITH THIS PLEASE HELP ME
Answer:
1a: f(x) = x³ -6x² +9x -4
1b: no breaks; the function is defined everywhere
2a: (-∞, 5]
2b: y = -3; y = -1
2c: x → -∞, y → -3; x → ∞, y → -1
Step-by-step explanation:
1A:The factored form of f(x) is ...
f(x) = (x -4)(x -1)²
f(x) = (x -4)(x² -2x +1) = x³ -2x² +x -4x² +8x -4
f(x) = x³ -6x² +9x -4
__
1B:The function h(x) is defined for all values of x to be either f(x) or g(x). The function f(x) is a polynomial function, so has no breaks in its domain. The function g(x) is defined for all values of x, so has no breaks in its domain.
There are no breaks in the domain of h(x).
__
2A:See the attachment for a graph.
-∞ < y ≤ 5 . . . . range of f(x)
__
2B:The asymptote as x → -∞ is the asymptote of the exponential function. The exponential term has an asymptote of y=0, but shifting it down 3 units means the asymptote is 0 -3:
x → -∞, y → -3 . . . . asymptote is y = -3
The asymptote as x → ∞ is the asymptote of the rational expression. That is the ratio of the leading terms: -x²/x² = -1.
x → ∞, y → -1 . . . . asymptote is y = -1
__
2C:See part B.
PLS PLS PLS PLS HELP :D <33
Answer:
Value of x = 3
m∠HEB=27°
Step-by-step explanation:
1) CEH and HEB are complementary angles, therefore both of their angles added together will be 90 degrees
2) Set the two equations added together equal to 90 and solve for x
19x+6+9x=90
28x=84
x=3
3) Plug in x into 9x to get HEB
9(3)=27
Divide.
1585 ÷ 25
63
6312
6325
63710
Answer:
The answer is 63 2/5
Step-by-step explanation:
Converting to mixed numbers divide 317 by 5.
5 goes into 31 at most 6 times and 5 goes into 17 at most 3 times.
The quotient of 317/5 is 63 with remainder of 2, so answer is 63 2/5.
Which property explains why these two expressions are equal? 7 + q + 4 = 4 + 7 + q
Martina's fish tank has 15 liters of water in it. She plans to add 5 liters per minute until the tank has at least 60 liters. What are the possible numbers of minutes
. :
Martina could add water?
Use t for the number of minutes
Write your answer as an incqua ty solved fort
Answer:
9 minutes
Step-by-step explanation:
60=15+5t
45=5t : subtract 15 from both sides
9=t : divide by 5 for both side
As a bowl of soup cools, the temperature of the soup is given by the twice-differentiable function H for 0[tex]\leq[/tex]t[tex]\leq[/tex]12, where H(t) is measured in degrees Celsius (C), and time t is measured in minutes. Values of H(t) at selected values of time t are shown in the table above.
a) Use the data in the table to approximate H'(5). Show the computations that led to your answer. Using correct units, explain the meaning of H'(5) in the context of the problem.
b) Is there a time t for 0[tex]\leq[/tex]t[tex]\leq[/tex]12 at which the temperature of the soup is 60C? Justify your answer.
c) The temperature of the soup is also modeled by the twice-differentiable function C for 0[tex]\leq[/tex]t[tex]\leq[/tex]12, where C(t) is measured in degrees Celsius (C), and time tis measured in minutes. It is known C(3)= 80 and the derivative of C is given by C'(t)= -3.6e-0.05t. Write an equation for the line tangent to the graph at t=3 and use it to approximate C(5).
d) Based on the model given in part c, at what rate, in degrees Celsius per minute minute, is the rate of change of the temperature of the soup changing at t=3 minutes?
The rate of change of temperature with time at a point in time is given by
the derivative of the function for the temperature of the soup.
The correct responses are;
a) H'(5) is approximately -2.6 degrees Celsius per minute.b) Yesc) The equation for the line tangent is y = -3.6·t + 90.8The approximate value of C(5) is 72.8 °Cd) The rate of change of the temperature of the soup at t = 3 minutes is -3.6 degrees Celsius per minute.Reasons:
a) From the data in the table, we have;
The approximate value of H'(5) is given by the average value of the rate of
change of the temperature with time between points, t = 3, and t = 8
Therefore;
[tex]\displaystyle H'(5) = \mathbf{\frac{H(8) - H(3)}{8 - 3}}[/tex]
Which gives;
[tex]\displaystyle H'(5) = \frac{80 - 67}{8 - 3} = \mathbf{2.6}[/tex]
Therefore, H'(5) = -2.6°C per minute
b) Given that the function is twice differentiable over the interval, 0 ≤ t ≤ 12, the function for the change in temperature is continuous in the interval 0 ≤ t ≤ 12
At t = 0, H(0) = 90 °C
At t = 12, H(12) = 58 °C
58 °C < 60 < 90 °CTherefore, there exist a temperature, of 60 °C between 90° C and 58 °C
c) The given derivative of C is, [tex]C'(t) = \mathbf{-3.6 \cdot e^{-0.05 \cdot t}}[/tex]
At t = 3, we have;
[tex]The \ slope \ at \ t = 3 \ is \ C'(3) = -3.6 \cdot e^{-0.05 \times 3} \approx -3.1[/tex]
Therefore, we have;
y - 80 ≈ -3.1 × (x - 3)
The equation for the tangent is; y = -3.6 × (x - 3) + 80
y = -3.6·x + 10.8 + 80 = -3.6·x + 90.8
The equation for the tangent is; y = -3.6·x + 90.8The value of C(5) is approximately, C(5) ≈ -3.6 × 5 + 90.8 = 72.8
C(5) ≈ 72.8°d) Based on the the model above, the rate at which the temperature of the
soup is changing at t = 3 minutes is -3.6 degrees per minute.
Learn more about calculus and concepts here:
https://brainly.com/question/20336420
c. A square that is 8 inches on a side is placed inside a rectangle that has a length of 24 inches and a width of 20 inches. What is the area of the region inside the rectangle that surrounds the square?
Area = length x width
Area of square = 8 x 8 = 64 square inches
Area of rectangle = 24 x 20 = 480 square inches
Area of rectangle surrounding the square = 480 - 64 = 416 square inches
Answer: 416 square inches
HELP!!
is {(-3,-6),(-2,-1),(-1,-0),(0,3),(1,15)} a function??
It's a function because we don't have any repeated x coordinates. Any given x input value leads to exactly one y output value.
The domain is {-3,-2,-1,0,1} which is the set of all x inputs.
The range is {-6, -1, 0, 3, 15} which is the set of y outputs.
11. m2 = 340 Find m 24 and explain how you know. (2 points)
1
X
3
Drawing not to scale.
Answer:
Angle 4 also has a measurement of 34 degrees because opposite angles of intersecting lines are congruent. In other words, angles 2 and 4 are congruent, so are angles 1 and 3.
What amount of a 40% acid solution must be mixed with 200 mL 10% solution to produce a 20% solution?
Answer:
Step-by-step explanation:
(x + 200)20 = 200(10) + x(40)
20x + 4000 = 2000 + 40x
2000 = 20x
X = 100 mL
How do you multiply fractions? And do we have to simplify them by any chance or no?
To multiply a fraction, imagine it this way. Start with 1/4. Then if you multiply 1/4 by 2 it would be 1/2.
If you have a quarter, and you times that quarter by 2, you have half a dollar.
It only needs to be simplified if you can simplify the fraction.
Answer:
Ok say your doing 1/4 * 2/4 you move the /4 over to the side and multiply 1 and 2 that would be 2 so then you put the the 2 on top of the /4 and you have 2/4… Now if you have odd numbers like 1/4 * 1/6 you would simplied the 6 and 4 what can go into (divide by the same number) 6 AND 4 both… 2 because so you change the 1/4 and 1/6 to a 1/2 * 1/2 those multiplied together equal 1/2
Step-by-step explanation: pls give brainleist and dont for get to leave a rating and heart
To make cupcakes Leah uses 1/2 cup of chocolate chips for evry 1 1/3 cups of batter if Leah uses 3/4 cups of chocolate chips how many cups of batter should she use
Answer:
2
Step-by-step explanation:
Leah uses 1/4 cup of chocolate chips for 2/3 cups of batter, so if Leah uses 3/4 cup of chocolate chips, she should use 2 cups of batter.
Which best describes reduced fractions that will always terminate?
A.
reduced fractions with denominators that are factors of only 5
B.
reduced fractions with denominators that are factors of 2 or 5
C.
reduced fractions with denominators that are factors of only 5 or 7
D.
reduced fractions with denominators that are factors of only 2 or 3
Answer:a
Step-by-step explanation:
Reduced fractions with denominators that are factors of 2 or 5. Therefore, the correct answer is option B.
Terminating decimals are integers with a definite or finite number of digits following the decimal point. Like fractions, decimal numbers are used to represent a portion of a whole. This course will concentrate on the type of decimal numbers known as terminating decimal numbers. The word 'terminate' means to put a stop to something. In decimal terms, it is a number that comes to an end.
Here are a few tips to assist you identify a terminating decimal number.
A non-rational number is never an ending decimal number.If the denominator of a simplified rational number can be expressed in the manner [tex]2^p5^q[/tex] or [tex]2^p[/tex] or [tex]5^q[/tex], where p, q N, then the number has a terminating decimal expansion.After the decimal point, a terminating decimal number always has a finite number of digits.Therefore, the correct answer is option B.
Learn more about the terminating fraction here:
https://brainly.com/question/5286788.
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Please look for the question in the picture.
plz help me to answer
Answer:
if you can only pick one it's e
Step-by-step explanation:
Im 90% sure a and c are both true answers while 70% sure that b and d are both true answers so unless someone says otherwise e is your best bet
3 2/3 + 2 3/5 + x = 8
Answer: x= [tex]-\frac {109}{15}[/tex]
Jasmine is scuba diving at an elevation of −68.4 feet when her friend signals to come higher. Jasmine makes three ascents, each an equal distance, to reach an elevation of −15.6 feet, where her friend is located. What was Jasmine's elevation after her first ascent? Enter your answer as a decimal in the box.
Answer:
-35.2
Step-by-step explanation:
-68.4-(-15.6)= (-52.8)
-52.8÷3=(-17.6)
-52.8-(-17.6)=-35.2
Answer:-35.2
Step-by-step explanation:
Zanele Situ is a disabled Olympic gold-medallist javelin champion. She threw the javelin a distance of 16,22 m in London at 2012 Olympics. She threw the javelin to a distance of 17,90 m in Rio at 2016 Olympics. By what percentage did the distance increase?
Answer:
10,4%
Step-by-step explanation:
The percentage change is found from ...
(amount of change)/(original amount) × 100%
(17,90 -16,22)/(16,22) × 100% = 1,68/16,22 × 100% ≈ 10,358% ≈ 10,4%
Which list of angle measures could be the angle measures of a triangle?
Need an answer right away for many points! I will report if it is not applicable.
Answer:
I don't know
Step-by-step explanation:
plus all of them = Answer
Answer:
Step-by-step explanation:
False Line of symmetry is x = -1
False The maximum of f(x) = 3
we can find the maximum of f(x) by putting it in vertex form (y - 3) = - 1(x + 7)² which tells us that the vertex is at (-7, 3)
True -7 < -1
Multiply:
5m^3 n^5 (25m^6 n)
A. 125m^18n^10
B. 30m^9 n^5
C. 30m^9 n^6
D. 125m^9 n^6
Answer:
D
Step-by-step explanation:
5m^3 n^5 (25m^6 n)
-->5m^3*25n^6m^6
-->125m^9 n^6
write 321.51 as word form
Answer:
three hundred twenty one and fifty one hundredths
Divide: 1/2÷1/10
SHOW WORK
Answer:
5
Step-by-step explanation:
1/2÷1/10=
1/2x10/1=
10/2=5
Answer:
the answer is 5
Step-by-step explanation:
keep change flip
1/2 x 10 =5
how much time should be allowed for a 392-km car trip if the car will be traveling at 120km/h
Answer:3hrs 16min
Step-by-step explanation:
392/120 = 49/15 hours = 3 hours + 4/15 hours = 3 hours + 4/15 x 60 min = 3 hours + 16 min
A statistics teacher was interested in the relationship between the number of days students waited to start a project
and the score that project received (out of 100 points). Information was collected on several students and was used
to obtain the regression equation ý= -3.64x + 96.5, where x represents the number of procrastination days and ý is
the predicted grade. What is the predicted grade of a student who procrastinated for 1 week?
O24.59
71.02
O 92.86
O. 96.5
Answer:
71.02
Step-by-step explanation:
x is the number of days
1 week = 7 days
-3.64 (7) + 96.5 = 71.02